Boundedness of Operators in Bilateral Grand Bebesgue Spaces with Exact\n and Weakly Exact Constant Calculation

2011/04/14 by E. Ostrovsky L. Sirota, Sirota, E. Ostrovsky L. · 4 citations
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1104.2963

openalex publication_date 2011/04/14 · openalex created_date 2022/09/01 · openalex updated_date 2026/07/28

Abstract

In this article we investigate an action of some operators (not necessary to\nbe linear or sublinear) in the so-called (Bilateral) Grand Lebesgue Spaces\n(GLS), in particular, double weight Fourier operators, maximal operators,\nimbedding operators etc. We intend to calculate an exact or at least weak exact\nvalues for correspondent imbedding constant. We obtain also interpolation\ntheorems for GLS spaces.We construct several examples to show the exactness of\noffered estimations. In two last sections we introduce anisotropic Grand\nLebesgue Spaces, obtain some estimates for Fourier two-weight inequalities and\ncalculate Boyd's multidimensional indices for this spaces.\n

Citations

• Nikol'skii-type inequalities for rearrangement invariant spaces
• Some Fractional Functional Inequalities and Applications to Some Constrained Minimization Problems Involving a Local Non-linearity

Cited by

• Necessary Conditions for Fractional Hardy-Sobolev's Inequalities
• Grand Lebesgue Spaces norm estimates for multivariate functional operations
• Mixed Lebesgue space norm Strichartz type estimation for solution of inhomogeneous parabolic equation, with constants evaluation
• Cesaro-Hardy operators on bilateral grand Lebesgue spaces

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